High entanglement generation and high fidelity quantum state transfer in a non-Markovian environment

This paper analyses a system of two independent qubits off-resonantly coupled to a common non-Markovian reservoir at zero temperature. Compared with the results in Markovian reservoirs, we find that much higher values of entanglement can be obtained for an initially factorized state of the two-qubit system. The maximal value of the entanglement increases as the detuning grows. Moreover, the entanglement induced by non-Markovian environments is more robust against the asymmetrical couplings between the two qubits and the reservoir. Based on this system, we also show that quantum state transfer can be implemented for arbitrary input states with high fidelity in the non-Markovian regime rather than the Markovian case in which only some particular input states can be successfully transferred.     

与热库耦合的光学腔内三原子间的纠缠动力学

研究了与热库耦合的光学腔中三个相互作用的二能级原子间的纠缠动力学.采用拉普拉斯变换和下限共生等方法,通过数值计算,分析了原子间三体纠缠的演化以及腔场与热库间的两体纠缠演化,讨论了各耦合参数对系统纠缠演化的影响.研究结果表明:原子间纠缠在短时间内随着原子间耦合强度的增加而增加,随原子与腔场耦合强度的增加而减小,在长时极限下趋于一稳定值;体系的非马尔科夫性由原子与腔场的耦合强度以及热库的谱宽度共同决定,当热库与腔场为强耦合时,原子与腔场组成的系统遵循非马尔科夫动力学,此时随着热库谱宽的增加,原子系统由非马尔科夫性变为马尔科夫性,随着谱宽的继续增加,原子与腔场组成的系统遵循马尔科夫动力学,原子系统又表现出非马尔科夫性;调整腔场与热库的失谐可以有效抑制热库耗散对纠缠衰减的影响.     

Modulation of Entanglement for Coupled Superconducting Qubits Under Non-Markovian Environment

The evolution of entanglement decoherence is investigated for a coupled superconducting qubit under non-Markovian environment by utilizing a commensal entanglement degree. The results show that, owing to the memory feedback effect of environment, the entanglement degree of the coupled qubits at the thermal equilibrium always monotonously tends to zero so that entanglement sudden death occurs briefly in the non-Markovian process. Different from the Markovian process, stronger the dissipation is, faster the entanglement sudden death is. We find that, furthermore, the interaction between the qubits results generally in reduction of entanglement degree in the quantum system. With some special initial states or initial phase angles, however, the influence of the interaction between qubits on the system entanglement degree can be avoided.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and single-sided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and singlesided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Dynamics of entanglement protection of two qubits using a driven laser field and detunings:Independent and common,Markovian and/or non-Markovian regimes

Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies.In this regard,we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent(Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field.Then,we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure.It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency,the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies(central detuning) in both non-Markovian and Markovian reservoirs.While the central detuning has a constructive role,the detuning between the qubit and the classical field(laser detuning) affects negatively on the entanglement protection.The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir.We demonstrate that,in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.     

Effect of entanglement embedded in environment on quantum non-Markovianity based on collision model

By means of collision models(CMs) where the environment is simulated by a collection of ancillas consisting of two entangled qubits, we investigate the effects of entanglement in the environment on the non-Markovianity of an open quantum system. Two CMs are considered in this study, in the first one the open quantum system S directly collides with the environment,while in the second one the system interacts with two intermediate qubits which, in turn, are coupled to the environment. We show that it is possible to enhance the non-Markovianity by environment entanglement in both models. In particular, in the second model, we show that the initial state of the auxiliary qubits can also affect the non-Markovianity of the system and there exists the optimal combination of the initial environmental state and the initial state of auxiliary qubits. In this case, the non-Markovianity can be greatly enhanced.     

Quantum Discord of two Coupled Qubits with Initial System-reservoir Correlation

Recently, the effect of initial qubit-reservoir correlation for two qubits in a common reservoir on the entanglement dynamics has been studied by Yan and Xia (Acta Sinica Quantum Optica 20, 16 2014). We extend their results and investigate how the initial qubit-reservoir correlation and dipole-dipole interaction between two qubits effect on dynamics of quantum discord in Markovian and non-Markovian regimes, respectively. The results show that in general, the larger initial qubit-reservoir correlation and dipole-dipole interaction can retard the decay of quantum discord. Besides, a combination of relatively strong dipole-dipole interaction and non-Markovian effect can efficiently protect quantum discord. Finally,thecomparisonbetweenevolutionsofquantumdiscordandentanglementisalsoconsidered.     

Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.     

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death(ESD) in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement,therefore in this case the entanglement cannot be optimized in the evolution process.     

Quantum correlations in non-Markovian environments

We have studied the analytical Markovian and non-Markovian dynamics of quantum correlations, such as entanglement, quantum discord and Bell nonlocalities for three noisy qubits. Quantum correlation as measured by quantum discord is found to be immune to death contrary to entanglement and Bell nonlocality for initial GHZ- or W-type mixed states.     

Entanglement and Decoherence of Coupled Superconductor Qubits in Contact with a Common Environment

The sudden death of entanglement is investigated for non-Markovian dynamic process of a pair interacting flux qubits under a thermal bath. The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that, for initially two-qubit entangled states, the sudden death of entanglement (ESD) always happens in the thermal reservoir, where the appearance of entanglement sudden death strongly depends on the environment. Especially, ESD of the qubits is easier to occur for non-Markovian process than for Markovian one.     

Non-Markovian Effects on Entanglement Dynamics of Three Qubits

We investigate entanglement dynamics of three independent qubits each locally interacting with a zero-temperature non-Markovian reservoir. The effects of environment's amount of non-Markovianity or parameters in initial states on the three-qubit entanglement dynamics are presented in detail. It is found that the entanglement of such a system revives after a finite dark period when a proper degree of non-Markovian is present. A deep comparison to that in two-qubit system is also made.     

Precision of estimation and entropy as witnesses of non-Markovianity in the presence of random classical noises

We investigate in detail the quantum Fisher information (QFI) behavior by examining a single qubit model in the presence of random classical noises in both Markovian and non-Markovian regimes. In particular, we precisely study the effects of noise switching rate ξ$\xi$ and qubit–environment coupling strength ν$\nu$ on the precision of estimation, when the qubit is subjected to random telegraph noise with a Lorentzian spectrum or colored noise with a spectrum of the form 1/f^α$1/f^{\alpha }$. In the Markovian regime, a monotone decay of the QFI with time is found, whereas for non-Markovian noise sudden death and revivals may occur. Despite these oscillations of the QFI in non-Markovian regime, we find that non-Markovian parameter γ=ξ/ν$\gamma =\xi /\nu$ is not the principal parameter controlling the collapse and revival of the QFI. In fact, in both Markovian and non-Markovian regimes, parameters ξ$\xi$ and ν$\nu$independently determine how the QFI varies. We also find that the QFI in the case of colored environments decreases when the number of fluctuators realizing the noise increases, and therefore the parameter estimation becomes more inaccurate. Furthermore, by analyzing the von Neumann entropy of the system density matrix, we illustratively unveil a fundamental relationship between the dynamics of this quantity and non-Markovian behavior in the presence of random classical noises. We also show that this result may lead to a better non-Markovianity interpretation, based on quantum memory effects. Moreover, we demonstrate the connection between the precision of parameter estimation and rising the non-Markovianity in our model where the environment is modeled as classical.     

Non-Markovianity in the presence of multiple thermal environments via collision model

By means of the collision model, we study the non-Markovianity of an open quantum system S being coupled to M thermal reservoirs. In our model, each reservoir is modeled as a chain of ancillas whose intracollisions account for the occurrence of non-Markovian dynamics. We show that by incorporating M reservoir ancillas into the system, the non-Markovian dynamics of S can be embedded in the extended system that experiences a completely Markovian dynamics. The number M of involved reservoirs can thus be identified as the memory depth and determines the degree of the non-Markovianity. In the equilibrium case with identical temperatures for all the reservoirs, we show that though the non-Markovianity is proportional to M in the zero and relatively low temperature regimes, in the relatively high temperature regime such proportional relation holds only for the weak intracollisions of the reservoir ancillas. In the nonequilibrium situation, we examine the effect of temperature difference of reservoirs on the non-Markovianity. Focusing on a simple situation with two reservoirs, we observe that the nonzero temperature difference has a significant impact on the non-Markovianity.     

Dynamics and Protection of the Relative Entropy of Coherence via Additional Non-interacting Qubits

We analytically study the dynamical behavior of the quantum coherence of a single-qubit coupled to a bosonic reservoir at zero temperature via plugging additional non-interacting qubits into the reservoir in both Markovian and non-Markovian regimes. The influences of detuning, memory effects and number of additional qubits on the dynamics of the quantum coherence are considered. It is found that, via increasing the number of the additional qubits in the reservoir, the quantum coherence can be preserved. Moreover, the method based on the combination of larger effective detuning, the stronger non-Markovian effects and the more number of additional qubits, can more effectively prevent the loss of the quantum coherence.

     

非马尔科夫环境下耦合超导量子系统纠缠演化的数值研究

基于耦合超导量子比特系统模型下,在非马尔科夫环境中利用共生纠缠的方法分析了耦合系统纠缠的产生及其动力学的演化。研究了不同初始纠缠态下的纠缠猝死(ESD)和纠缠再生(ESB)现象;主要分析了系统耦合强度、库的截止频率与系统的振荡频率间的比值、温度和约瑟夫森能级差对纠缠演化的影响。结果表明:系统纠缠取决于初始纠缠态和系统的耦合强度J,并且通过调节以上非马尔科夫环境的相干参数可以延长解纠缠时间来确保量子计算过程中的应用和量子信息的实现。     

Rise of quantum correlations in non-Markovian environments in continuous-variable systems

We investigate the time evolution of quantum correlations, which are measured by Gaussian quantum discord in a continuous-variable bipartite system subject to common and independent non-Markovian environments. Considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that quantum correlations can be created during the non-Markovian evolution, which is different from the Markovian process. Furthermore, we find that the temperature is a key factor during the evolution in non-Markovian environments. For common reservoirs, a maximum creation of quantum correlations may occur under an appropriate temperature. For independent reservoirs, the non-Markovianity of the total system corresponds to the subsystem whose temperature is higher. In both common and independent environments, the Gaussian quantum discord is influenced by the temperature and the photon number of each mode.     

Entanglement and decoherence of coupled superconductor qubits in a non-Markovian environment

The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entanglement sudden death (ESD) always happens in the thermal reservoir, where its appearance strongly depends on the environment. In particular, ESD of the qubits occurs more easily for the non-Markovian process than for the Markovian one.